let N be non empty with_non-empty_elements set ; :: thesis: for S being non empty stored-program halting IC-Ins-separated definite AMI-Struct of N
for p being NAT -defined the Instructions of b₁ -valued finite Function
for s being State of S
for i being Element of NAT st p halts_at IC (Comput p,s,i) holds
Result p,s = Comput p,s,i
let S be non empty stored-program halting IC-Ins-separated definite AMI-Struct of N; :: thesis: for p being NAT -defined the Instructions of S -valued finite Function
for s being State of S
for i being Element of NAT st p halts_at IC (Comput p,s,i) holds
Result p,s = Comput p,s,i
let p be NAT -defined the Instructions of S -valued finite Function; :: thesis: for s being State of S
for i being Element of NAT st p halts_at IC (Comput p,s,i) holds
Result p,s = Comput p,s,i
let s be State of S; :: thesis: for i being Element of NAT st p halts_at IC (Comput p,s,i) holds
Result p,s = Comput p,s,i
let i be Element of NAT ; :: thesis: ( p halts_at IC (Comput p,s,i) implies Result p,s = Comput p,s,i )
assume A1: p halts_at IC (Comput p,s,i) ; :: thesis: Result p,s = Comput p,s,i
then p halts_on s by AMI_1:83;
hence Result p,s = Comput p,s,i by A1, Th85; :: thesis: verum